Word Problems Involving Ratios and Rates

Front

What is a ratio?

Back

A ratio is a comparison of two quantities that shows the relative size of one quantity to another, often expressed as 'a to b' or a:b.

Front

What is a rate?

Back

A rate is a specific kind of ratio that compares two different units, such as miles per hour or price per item.

Front

How do you find the unit rate?

Back

To find the unit rate, divide the quantity by the number of units. For example, if a car travels 300 miles in 5 hours, the unit rate is 300 miles ÷ 5 hours = 60 miles per hour.

Front

If a car travels 420 miles in 8 hours, how do you calculate the distance it will travel in 12 hours?

Back

First, find the unit rate: 420 miles ÷ 8 hours = 52.5 miles per hour. Then multiply the unit rate by 12 hours: 52.5 miles/hour × 12 hours = 630 miles.

Front

What is the formula to solve for x in a proportion?

Back

In a proportion, you can use cross-multiplication: if a/b = c/d, then ad = bc.

Front

If Pat needs 14 sticks of pepperoni for 28 pizzas, how do you find the number of sticks needed for 36 pizzas?

Back

Set up a proportion: 14 sticks/28 pizzas = x sticks/36 pizzas. Cross-multiply and solve for x: x = (14 sticks × 36 pizzas) ÷ 28 pizzas = 18 sticks.

Front

How do you convert a ratio to a fraction?

Back

To convert a ratio to a fraction, write the first quantity as the numerator and the second quantity as the denominator. For example, the ratio 3:4 can be written as the fraction 3/4.

Front

What is the difference between a ratio and a fraction?

Back

A ratio compares two quantities, while a fraction represents a part of a whole. A ratio can be expressed as a fraction, but not all fractions are ratios.

Front

If a bird flies 35 meters in 10 seconds, how do you find the time to fly 14 more meters?

Back

First, find the speed: 35 meters ÷ 10 seconds = 3.5 meters/second. Then, use the formula time = distance ÷ speed: time = 14 meters ÷ 3.5 meters/second = 4 seconds.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, 1/2 = 2/4 is a proportion.